Models and methods in hillslope profile morphometry

Abstract

This thesis considers and evaluates mathematical models and methods of data analysis used in the quantitative study of hillslope profile form. Models of hillslope profiles are brought together in a critical and comprehensive review. Modelling approaches are classified using five dichotomies (static/dynamic, deterministic/ stochastic, phenomenological/representational, analytical/ simulation, discrete/continuous). Profile data to serve as examples were collected using a pantometer in a 100 km(^2) square centred on Bilsdale in the North York Moors. Geomorphological interpretations put forward for this area include theses of profound lithological influence, polycyclic denudation history, proglacial lake overflow channels and profound cryonival influence. Profile dimensions, profile shapes, angle and curvature frequency distributions and bedrock geology can be related via a fourfold grouping of profiles. The use of quantile-based summary measures and of a method of spatial averaging and differencing are advocated and illustrated. Autocorrelation analysis of hillslope angle series appears to be of limited geomorphological interest, as autocorrelation functions tell a story of overall profile shape, which can be measured more directly in other ways. Problems of non stationarity and estimator choice deserve greater emphasis. Methods of profile analysis previously proposed by Ahnert, Ongley, Pitty and Young are all unsatisfactory. A method based on additive error partition and nonlinear smoothing is proposed as an interim alternative, and results related to bedrock geology. An approach to model fitting is outlined which treats specification, estimation and checking in sequence. A power function due to Kirkby is used as an example and fitted to field data for components. The exercise works well if regarded as a minimum descriptive approach but much greater difficulties arise if process interpretation is attempted.